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dybincka [34]
2 years ago
12

Help please I will mark brainliest

Mathematics
1 answer:
NISA [10]2 years ago
5 0

(a) Fermat's little theorem states that for any prime p, we have

a^{p-1} \equiv 1 \pmod p

for any integer a. Then

999,999 \equiv 1,000,000 - 1 \equiv 10^6 - 1 \equiv 1 - 1 \equiv 0 \pmod 7

so 7 does indeed divide 999,999.

(b) Generalizing, we have

10^{12n} - 1 \equiv \underbrace{999\ldots999}_{12n \text{ nines}} \equiv (10^n)^{12} - 1 \equiv 0 \pmod {13}

for positive integer n. Now, since 1 = 1001 - 1000 and -1\equiv1000\pmod{1001}, it follows that 10^3 is its own inverse modulo 1001, i.e.

10^3 x \equiv 1\pmod{1001} \implies x = 10^3

This means

10^{12n} \equiv (10^3\times10^3)^{2n} \equiv 1^{2n} \equiv 1\pmod{1001} \\\\ \implies 10^{12n} - 1 \equiv 0 \pmod{1001}

which is what we wanted to show.

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Answer:

25/500 or 5% said 'other'

Step-by-step explanation:

55% = 275 (dog)

1/10 = 50 (cat)

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Total = 475

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3 years ago
Rodrigo applied for a $14,000 loan at an interest rate of 5.4% for 6 years. Use the monthly payment formula to complete the stat
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Answer:

A= $19354.71

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Step-by-step explanation:

$14,000 loan at an interest rate of 5.4% for 6 years.

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A= p(1+r/n)^(nt)

P= $14000

r= 0.054

t = 6

n = 6*12 = 72

A= 14000(1+0.054/72)^(72*6)

A= 14000(1+ 0.00075)^(432)

A= 14000(1.00075)^(432)

A= 14000(1.38247941)

A= 19354.71

A= $19354.71

3 0
3 years ago
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Step-by-step explanation:

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x = 96/8

So, x = 12

Hence the value one unit of the bar model is 12

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